# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.8)

8.

The largest 4 digit number exactly divisible by 88 is:

 [A]. 9944 [B]. 9768 [C]. 9988 [D]. 8888 [E]. None of these

Explanation:

```Largest 4-digit number = 9999

88) 9999 (113
88
----
119
88
----
319
264
---
55
---

Required number = (9999 - 55)
= 9944.
```

 Rashmi said: (Feb 11, 2011) How to take 9999 only ?

 Suhas said: (Feb 12, 2011) Because 9999 is the greatest 4 digit number.

 Saranya said: (Jun 25, 2011) How it will be possible by taking this 9999. Explain me please.

 Goutham said: (Jul 4, 2011) The largest 4-digit no. is 9999. when we divide it by 88 we got remainder as 55. It means that 9999 is 55 more than a number that is completely divisible by 88. So we have to subtract that extent 55 from 9999 to get actual number.

 Vasanthi said: (Jul 15, 2011) Hi! its a simple method to clear. That is It s some more difficult to divide by 88. So to solve the problem, just divide the no by 8 and 11. Because 88=8*11. Check it.

 Mahender Reddy said: (Aug 16, 2011) Ya you are correct vasanthi.

 Akanksha said: (Jun 8, 2012) No Vasanthi. If we divide 9988 by 8 and 11 then also its fully divisible and our answer comes wrong. Not a correct method. You urself check for all numbers.

 Sitam said: (Aug 26, 2012) To akansha it is a correct method.formula of divisible by 11 is odd place no=even place number and by 8 is the sum of first 3 digit must be divisible by 8.Here greatest number is given 9944 which fulfil the two condition above.Although others are also fulfil the conditions but they are not greatest.

 Sanjay Shokeen said: (Aug 26, 2012) I can't understand why are you take 9999.

 Uday said: (Oct 2, 2012) @sanjay. The greatest 4 digits number i.e. 9999.

 Nabarun said: (Feb 7, 2013) The largest 4 digit number is 9999. As we have to check largest 4 digit number divisible by 88 we can exclude options b and d. 9988 is not divisible by 8. So answer is 9944.

 Saravanan said: (Feb 17, 2013) Another simple method. Divide the largest number by the given number.i.e 9999/88 which is equal to 113.625 Now multiply the exact number (number before the .(dot) i.e 625 (113*88). The result would be 9944. Also we are taking 9999 because the largest number from 01 to 1000 (the numbers given are between 01 to 1000) is 9999.

 Balaji said: (Sep 8, 2013) 9944. (9+4)-(9+4)=0 or div by 11. Last 3 digit 944 div by 8. So it is div by 88.

 Karthika said: (Dec 9, 2014) 4 digits no 9999 k. But how is it 113, 88, 119, 319? Please explain sir.

 Pravallika said: (Dec 17, 2014) I agree with @Vasanthi because give no should be divisible by both 11 and as well as 8. But we should take the rule for divisibility of 8 only not 4*2. i.e. no formed by last 3 digit no should be divisible by 8.

 Siva said: (Apr 29, 2015) @Balaji, All numbers in that option are divisible by 11 and option B. And option D are also divisible both 11 and 8 then how you can say that above method is correct?

 Srija said: (May 15, 2015) The largest no 9999/88 = 113. And to compared to the values, /88 = 113. 9944/88 = 113. 9768/88 = 111. 9988/88 = 113.5. 8888/88 = 101. So they equal values to show the result in 9944.

 Prema said: (Jun 12, 2015) 88=11*8. If 9944 is divisible by 8 and 11. It is also divisible by 88. 9944/8=1243, 9944/11=94. So it is divisible by 88.

 Sameer said: (Jul 6, 2015) 88 - 9999 = 9911. So how it came 119. Please explain it.

 Mahendra said: (Sep 27, 2015) Why can't we do it by splitting the number? 88 = 11*4*2. Why can't we take the largest number that is divisible by 11, 4 & 2? (This method was used to solve problem no:6).

 Shashank said: (Oct 9, 2015) @Vasanti is right. 9999/11 = 909, 909/8 = 113 and reminder is 5. Now multiply 5 by 11, because 88 has been split into 11 and 8 and 5*11 = 55, 9999-55 = 9944 is your answer.

 Naveen said: (Dec 7, 2015) 101^100-1 is divisible by?

 P.Dhana Lakshmi said: (Aug 5, 2016) I can't understand. Please tell me in another way.

 Shiva said: (Aug 24, 2016) 9999/88 = 113.625 Take the integer part only i.e 113 and multiply it by 88 (113 * 88 = 9944) So, 9944 is the largest 4 digit no exactly divisible by 88 simple.

 Arjun said: (Sep 28, 2016) Why cannot we do it by splitting the number? 88 = 11 * 4 * 2.

 Nidhin M Z said: (Oct 6, 2016) The largest no 9999/88 = 113. And to compared to the values, /88 = 113. 9944/88 = 113. 9768/88 = 111. 9988/88 = 113.5. 8888/88 = 101. So, they equal values to show the result in 9944.

 Rakeshnartu@Gmail.Com said: (Nov 5, 2016) Apply divisibility test of 8 for this problem the last three digits should be divisible by 8.

 Manyamuma said: (Nov 21, 2016) Why can not we do it by splitting the number 88 as 11 * 4 * 2?

 Raksha said: (Mar 23, 2017) How 9999 is a largest 4 digit number? Please someone help me.

 Rohit said: (Apr 8, 2017) Becoz in 4 digits number the 9999 is last and largest.

 Jayadev Sahoo said: (May 10, 2017) The number is also divisible by 11, 8, then divisible by 88. All number divisible by 11, 8 expect 9988 then the largest number is 9944.

 Shubham Pandey said: (May 20, 2017) The least number of five digits exactly divisible by 88 is? Please solve it.

 Binit said: (Aug 1, 2017) 88=11*8. 9944 have three digit number is 944 which is divisible by 8. and when we substract its attractive number it is =0 so, it is divisible by 11 so it answers.

 Abhishek Kumar said: (Aug 26, 2017) It is one of the best ways to solve this type of questions that you take4 digit largest number 9999. Then divide it by 88 but brake 88 in 8*11 then divide 9999 by 11 you will get 99. Then you will divide it by 8 you will get 5 as remainder then multiple remainders with 11 the total remainder is 55 so 9999-55=9944 is the answer. 9999/8*11=99/8=5*11=55. 9999-55=9944.

 Sushma said: (Sep 8, 2017) But the divisibility rule of 8 is last 3 digits should be divisible by 8 not the first 3 digits.

 Gitanjali said: (Jan 4, 2018) What if the question is smallest 4 digit number. I know we need to divide with 1000 but what we'll do after divisions like here it is 9999 - 55, what will be there?

 Ade said: (Jan 15, 2018) How did you get 264?

 Sowmiya said: (Jan 18, 2018) Why we take (9999-55)?

 Megha said: (Feb 2, 2018) 9944, 9988, 8888 all three number divisible by 2 and 11, so how we can find the greatest number?

 Ramith said: (Feb 17, 2018) When 9999/88 = remain 55 how is that 9999/88 = 116.625?

 Biswarupa Rout said: (May 11, 2018) Why you take 9999? Please explain.

 Shivraj said: (Jun 13, 2018) Because, 9999 is largest four digit number, whenever we devide it by 88 reminder remains 55, when we substract 55 from 9999 we get exact number which is divisible by 88 i.e. 9944.

 Murali Goud said: (Jul 28, 2018) We can write 88=11*8=11*4*2. So the 4 digit number must be divisible by all the digits i.e 11,4,2. But where am I confusing is the number 9988 is divisible by all the numbers i.e 11,4,2 but it is not divisible by 88. Why? The method is wrong or write? Can anyone suggest?

 Sudeshna said: (Aug 5, 2018) @Biswarup rout. A. 4 digit number has Th H T and One's place. Under each place value, the minimum value we can write is 0 and the maximum value is 9. Hence, if ones, tens, hundred and Thousand all have 9, then 9999 is the largest 4 digit number. Similarly, largest 5 digits will have 99999 so on and so forth. The smallest 4 digit will be 1000. Smallest 5 digit will be 10000.

 Pankaj Namekar said: (Aug 28, 2018) 9988 is the answer because; 88= (11*2*4). 9988 is completely divisible by 88.

 K .Srikanth said: (May 6, 2019) Largest 4 digit number is 9999. In the question they asked what is the largest 4digit number divisible by 88 (just we assume largest number is 9999).

 Aditya said: (Sep 25, 2019) The easiest way to understand this is Euclid's division lemma. Dividend = divisior * quatient+remainder. So 9999 = 88 * 113 + 55.. 9999-55 = 88 * 113 = 9944 = 9944.

 Ruchita said: (Oct 11, 2019) Here is an easier method. First, divide 9999 by 11(9999/11=909). Then divide 909 by 8 (909/8 = we get 5 reminder). But 5 is for 909. 909=5. 9999=?. Then 9099*5/909. We can get 55 reminder by this easy method.

 Aarya said: (Oct 21, 2019) Because it is the biggest 4 digit number -9999.

 Charan said: (Jul 11, 2020) Simple trick to solve. Take unit digit method. 88 * 88 take unit place and multiple it we get 64. We check the options which option unit place is 4. There is only one option unit digit is 4 ie. Option A.

 Nikita said: (Jul 16, 2020) 9768 รท 88 = 111. 9768 is a greater number. So, I think B is the correct answer.

 Bhuvi said: (Oct 27, 2020) 1st 9999 divided by 88 then remaining answer is 55 then 9999 - 55 = 9944.

 Kuldeep said: (Jul 10, 2021) How came 119? Please explain.

 Darshan Prajapati said: (Sep 11, 2021) How it is correct? because above in the example no. 6 method is to split the number & then check the number either diveded by all or not. And same method if we applied in this example (11*2*4) = 88. So, 9988 is divided by all 11, 2, & 4. Please anyone clarify this.